Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 7 summary

HOW SAMPLE PROPORTIONS VARY AROUND THE POPULATION PROPORTION
The sample distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. The population distribution from which you take the sample. Values of its parameters are fixed, but usually unknown. Data distribution is the distribution of the sample data. It is also called sample proportion. Sampling distribution is the distribution of a sample statistic such as a sample proportion. Sampling distributions describe the variability that occurs from sample to sample.

For a random sample size n from a population with proportion p of outcomes in a particular category, the sampling distribution of the sample proportion in that category has:

 and 

For a large sample size n, the binomial distribution has a normal distribution. The central limit theorem states that the sampling distribution of the sample mean x̄ often has approximately a normal distribution. This result applies no matter what the shape of the population distribution from which the samples are taken. The standard deviation of the sampling distribution has the following formula:

The larger the sample, the closer the sample mean tends to fall to the population mean.

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Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Book summary
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